Methods and apparatus for active front end filter capacitor degradation detection

ABSTRACT

Apparatus and methods are provided for detecting degradation of delta-connected filter capacitors in an active front end (AFE) power converter, in which delta circuit capacitor leg currents are calculated based on measured branch circuit currents, and filter capacitor impedance values are computed based on the calculated leg currents as well as measured line-to-line voltages and corresponding phase angles for comparison with one or more thresholds to selectively detect degradation of the filter capacitors. Further apparatus and methods are provided for detecting degradation of Y-connected filter capacitors by computation of fundamental frequency RMS impedance values as ratios of RMS capacitor voltages and RMS circuit branch currents, and comparison of the calculated RMS impedance values with one or more thresholds.

BACKGROUND

Motor drives and other power conversion systems operate using power fromAC power sources, and typically include an input filter to reduceswitching noise associated with operation of the power converter, andparticularly to control total harmonic distortion (THD) generated byhigh frequency operation of certain active front end (AFE) rectifiers.In particular, many power conversion systems utilize inductor-capacitor(LC) or inductance-capacitance-inductance (LCL) input filter circuitryassociated with each AC input phase to control the harmonic content of aconnected power grid. Such filter circuits are subject to damage ordegradation of the filter capacitors. Filter capacitor degradation, inturn, may be costly in terms of replacement component costs, labor forinspection and replacement, as well as downtime for the power conversionsystem and any associated machinery. Thusfar, however, assessing theperformance and any degradation in the input filter capacitors has beendifficult, and initial capacitor degradation may not be identifiable byvisual inspection by service personnel. Certain conventional powerconverters employ fuses in line with the filter circuit capacitors, butin practice the fuses either do not open quickly enough to preventcapacitor degradation or open frequently in normal operation withhealthy capacitors, whereby excessive system downtime results.Accordingly, a need remains for improved filter capacitor degradationprediction or detection apparatus and techniques for use with an activefront end power converters.

SUMMARY

Various aspects of the present disclosure are now summarized tofacilitate a basic understanding of the disclosure, wherein this summaryis not an extensive overview of the disclosure, and is intended neitherto identify certain elements of the disclosure, nor to delineate thescope thereof. Rather, the primary purpose of this summary is to presentvarious concepts of the disclosure in a simplified form prior to themore detailed description that is presented hereinafter. The presentdisclosure provides methods and apparatus for active front end (AFE)power converter filter capacitor degradation detection in whichline-to-line voltage and circuit branch currents are measured, anddelta-connected filter capacitor impedances are calculated and comparedwith one or more thresholds without requiring direct measurement of thecapacitor currents. The disclosure thus presents a significant advanceover conventional capacitor degradation prevention or detectiontechniques since no fuses are used and the onset of degradation can beassessed prior to system damage. The detected degradation condition canbe used, in turn, to provide a system alert or warning and/or to shutdown the power conversion system.

A power conversion system is disclosed, including an active front endrectifier and an input filter circuit including three series circuitswith one or more associated filter inductors coupled between acorresponding system power input phase and a corresponding rectifierinput phase. The filter circuit further includes three capacitor circuitbranches individually connected to one of the corresponding seriescircuits, as well as three filter capacitors connected in a deltaconfiguration. A feedback circuit senses line-to-line voltages acrossthe filter capacitors, as well as filter circuit branch currents. Thepower converter further includes a degradation detection system thatcalculates fundamental frequency filter capacitor impedance values basedat least partially on the line-to-line voltages and the filter circuitbranch currents, and selectively detects degradation of one or more ofthe filter capacitors according to the calculated impedance values.

In certain implementations, the individual series circuits of the inputfilter circuit include first and second filter inductors, with theindividual capacitor circuit branches being connected to the nodejoining the first and second filter inductors of the correspondingseries circuit. The detection system in certain implementations filtersthe line-to-line voltage and the filter circuit branch currents toobtain values at the input power fundamental frequency, and calculatesRMS values for use in determining the fundamental frequency filtercapacitor impedance values. In certain embodiments, moreover, the systemuses formulas for calculating the capacitor impedances which incorporatea ratio determined according to an artificial resistive circuitconnected in a delta configuration, such that the formulas involve onlythe fundamental frequency RMS line-to-line voltages and filter circuitbranch current values, as well as phase angles between the line-to-linevoltages. In certain implementations, for example, the system includes azero-crossing detection circuit to measure the phase angles between thevoltages, or the phase angles may be assumed (e.g., 120° and 240°).

A method is provided for detecting filter capacitor degradation in amotor drive in accordance with further aspects of the disclosure,including measuring line-to-line voltages across delta-connected filtercapacitors as well as measuring filter circuit branch current values.The method further includes calculating fundamental frequency filtercapacitor impedance values according to the measured voltages andcurrents, and comparing the calculated capacitor impedances with atleast one threshold. Degradation of one or more of the filter capacitorsis selectively detected at least partially according to the comparisonof the calculated impedance values with the threshold. Certainembodiments of the method include issuing an alert or shutting down themotor drive based on the threshold comparison. In certain embodiments,moreover, the method includes filtering the measured voltages andcurrents to obtain filtered values at the AC input fundamentalfrequency, as well as computing RMS values for calculating thefundamental frequency filter capacitor impedance values.

Further aspects of the present disclosure provide apparatus andtechniques for detecting degradation of Y-connected filter capacitors,in which capacitor voltages are sensed, such as between a branch circuitand a common connection point of the Y-connected filter capacitors, andthe voltages are filtered to provide fundamental frequency capacitorvoltage values, and RMS values are computed therefrom. Likewise, thefilter branch circuit currents flowing through the filter capacitors aremeasured and fundamental frequency RMS values thereof are obtained. Thefilter capacitor impedance values are then calculated as a ratio of thefundamental frequency RMS voltage to the fundamental frequency RMScurrent, and the resulting calculated filter capacitor impedance valuesare compared with one or more thresholds for selective detection offilter capacitor degradation.

In accordance with further aspects of the present disclosure, computerreadable mediums are provided with computer executable instructions forperforming the filter capacitor degradation detection methods.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description and drawings set forth certain illustrativeimplementations of the disclosure in detail, which are indicative ofseveral exemplary ways in which the various principles of the disclosuremay be carried out. The illustrated examples, however, are notexhaustive of the many possible embodiments of the disclosure. Otherobjects, advantages and novel features of the disclosure will be setforth in the following detailed description when considered inconjunction with the drawings, in which:

FIG. 1 is a schematic diagram illustrating an exemplary active front end(AFE) motor drive with an input LCL filter including delta-connectedfilter capacitors as well as filter capacitor degradation detectionapparatus in accordance with one or more aspects of the presentdisclosure;

FIG. 2 is a schematic diagram illustrating another AFE motor driveconnected to a power source through a transformer, including a CL inputfilter with delta-connected filter capacitors and filter capacitordegradation detection apparatus according to the present disclosure;

FIG. 3 is a schematic diagram further illustrating various measured andcomputed voltages and currents in the LCL filter of FIG. 1 as well ascomputation of leg and branch currents in an artificial delta-connectedresistive circuit for computing a correction factor ratio in accordancewith the present disclosure;

FIGS. 4 and 5 show a flow diagram illustrating an exemplary process fordetecting AFE filter capacitor degradation in accordance with furtheraspects of the disclosure;

FIG. 6 is a schematic diagram illustrating further details of theexemplary impedance computation in the degradation detection apparatusof FIGS. 1 and 2;

FIG. 7 is a graph showing exemplary line-to-line voltage waveforms andcorresponding phase angles in the systems of FIGS. 1 and 2;

FIG. 8 is a schematic diagram illustrating another exemplary AFE motordrive with an input LCL filter with Y-connected filter capacitors, and adegradation detection system according to further aspects of the presentdisclosure;

FIG. 9 is a schematic diagram further illustrating various measured andcomputed values in the LCL filter of FIG. 8; and

FIG. 10 is a flow diagram illustrating an exemplary process fordetecting or predicting AFE filter capacitor degradation in the systemof FIGS. 8 and nine according to further aspects of the disclosure.

DETAILED DESCRIPTION

Referring now to the figures, several embodiments or implementations arehereinafter described in conjunction with the drawings, wherein likereference numerals are used to refer to like elements throughout, andwherein the various features are not necessarily drawn to scale.Techniques and apparatus are disclosed for detection of degradation inpower conversion system filter capacitors connected in a deltaconfiguration. These aspects of the disclosure find utility inassociation with active front end (AFE) motor drives as well as otherforms of power conversion systems. In addition, although illustrated inthe context of a three-phase input devices, the disclosed concepts canbe employed in power conversion systems having any number of inputphases in which an input filter includes at least one delta-connectedfilter capacitor circuit.

The disclosed techniques and apparatus advantageously facilitatecomputation and monitoring of input filter capacitor values (i.e.,capacitance) and changes therein to predict or detect componentdegradation without requiring direct measurement of current flowingthrough the monitored capacitors. In this regard, packaging and otherphysical constraints may, in some systems, prevent incorporation ofdirect current sensors in the delta circuit branch legs, and/orprovision of such sensors may be cost prohibitive. Using the disclosedtechniques, however, the current flowing into branches connected to thedelta configuration of three filter capacitors can be used along withmeasured line-to-line voltages across the filter capacitors and measuredor assumed voltage phase angles for computation of the individual filtercapacitance values. With these, a comparison can be made with one ormore threshold values in order to assess potential degradation of theindividual filter capacitors, and a determination can be made as towhether one or more of these components are degrading. The degradationdetection, moreover, can be used to initiate any appropriate remedial orreporting action. In this manner, the present disclosure avoids the overinclusive or under inclusive nature of protective fuses previously usedin line with filter capacitors, and also advantageously facilitatesearly identification of the onset of component degradation indelta-connected input filter capacitors. This, in turn, can be used tominimize system downtime and reduce or mitigate maintenance costsassociated with a motor drive or other power conversion system.

Referring initially to FIGS. 1 and 2, FIG. 1 illustrates an exemplarymotor drive 10 with a three phase AC input 4 receiving input power froma three-phase source 2, where the drive 10 includes a rectifier 30, anintermediate DC link circuit 40 and an output inverter 50 providingvariable frequency, variable amplitude AC output power to drive a motorload 6. Although illustrated and described in the context of a motordrive type power conversion system 10, the various disclosed conceptscan be employed in other forms of power conversion systems, whetherproviding an AC output or a DC output to drive a motor or other type ofload. The drive input 4 has three input phase terminals which areconnected through an LCL input filter circuit 20 to the AC input of theswitching (active front end) rectifier 30. The switching rectifier 30includes switching devices S1-S6 individually coupled between acorresponding one of the AC input phases (u, v, w) and a correspondingDC bus terminal (+ or −) of the DC link circuit 40. A drive controller60 includes a rectifier switching controller 62 that provides rectifierswitching control signal 62 a to the rectifier switches S1-S6 to causethe rectifier 30 to convert received three-phase AC input power toprovide a DC voltage Vdc across a DC bus capacitance Cdc of the linkcircuit 40 using any suitable pulse width modulation (PWM) technique.The inverter 50 receives DC input power from the link circuit 40 andincludes inverter switches S7-S12 individually coupled between one ofthe positive or negative DC bus terminals and a corresponding outputphase connected to the motor load 6. The inverter switches S7-S12 areoperated according to inverter switching control signals 66 a providedby an inverter switching component 66 of the drive controller 60, whichgenerates the signals 66 a according to any suitable pulse widthmodulation technique to convert DC power from the link circuit 40 toprovide variable frequency, variable amplitude AC output power to themotor load 6. The switching rectifier 30 and the inverter 50 may employany suitable form of switching devices S1-S12 including withoutlimitation insulated gate bipolar transistors (IGBTs), siliconcontrolled rectifiers (SCRs), gate turn-off thyristors (GTOs),integrated gate commutated thyristors (IGCTs), etc.

As seen in the example of FIG. 1, the LCL filter circuit 20 includesthree series circuits individually connected between the power converterinput 4 and the corresponding phase of the rectifier AC input. Eachseries circuit includes a pair of series-connected filter inductors,with the first circuit including inductor La (e.g., a 3% inductor)connected between the first power converter input terminal and a firstintermediate node “a”, as well as a second filter inductor (e.g., a 9%inductor) Lu connected between the intermediate node a and a firstrectifier AC input node “u”. Similarly, the second series circuitincludes a first inductor Lb connected between the second motor driveinput and a second intermediate node “b” and a second inductor Lvconnected between the node b and the second rectifier input “v”, as wellas a third series circuit with first and second inductors Lc and Lwjoined by a third intermediate node “c”. In addition, the filter circuit20 includes three capacitor circuit branches 22 a, 22 b and 22 crespectively connecting the nodes a, b and c to a delta configuration ofthree filter capacitors Cab, Cbc and Cca. In this delta-connectedcapacitor circuit, each filter capacitor C is connected to two of thecapacitor circuit branches 22 as shown.

FIG. 2 illustrates an alternate embodiment in which a CL filter circuit20 is provided for interfacing the motor drive 10 with the power source2 through a transformer 3. In this example, the first filter inductorsLa, Lb and Lc are omitted due to the inductance of the secondarywindings of the transformer 3, and the input terminals 4 are connecteddirectly to the inductors Lu, Lv and Lw at the nodes a, b and c,respectively.

As seen in FIGS. 1 and 2, moreover, the motor drive 10 includes adegradation detection system 70 coupled with the filter circuit 20, aswell as a feedback circuit which senses line-to-line voltages V_(c.ab),V_(c.bc) and V_(c.ca) across the filter capacitors Cab, Cbc and Cca, forexample, by sensing the voltages at the branch circuits 22 asillustrated. In addition, the feedback circuit includes current sensorscoupled to the branch circuits 22 to sense the filter circuit branchcurrents I_(ca), I_(b) and I_(c) flowing in the associated capacitorcircuit branches 22 a, 22 b and 22 c. The degradation detection system70 can be any suitable hardware, processor-executed software,processor-executed firmware, programmable logic, analog circuitry, etc.which provides the described filtering, RMS computations, impedancecomputations and threshold comparison functionality as set forth herein,and may be operative using one or more processor elements executingcomputer executable instructions stored in an electronic memory of thesystem 70. As seen in FIGS. 1 and 2, the degradation detection system 70may include one or more components, which may be implemented as softwareand/or firmware components in execution, programmable logic, etc.,including a low pass filter/RMS computation component 72, an impedancecomputation component 74, as well as comparison logic operating tocompare one or more computer calculated values to one or more thresholds76. In addition, the degradation detection system 70 may provide adetection output signal or value 78 indicating that degradation of oneor more of the filter capacitors Cab, Cbc and/or Cca has been detectedby the system 70. In one implementation, as illustrated, the degradationdetection signal 78 may be provided to the motor drive controller 60 toinitiate one or more actions, such as shutting down the motor drive 10and/or providing an alert or warning signal or other indication, forinstance, to a user interface associated with the motor drive 10 and/orto a connected network (not shown).

In operation, the degradation detection system 70 is configured tocalculate fundamental frequency filter capacitor impedance valuesZ_(ab.60Hz), Z_(bc.60Hz) and Z_(ca.60Hz) based at least in part on themeasured line-to-line voltages V_(c.ab), V_(c.bc) and V_(c.ca) andaccording to the sensed filter circuit branch currents I_(c.a), I_(c.b)and I_(c.c). In addition, the system 70 selectively detects degradationof one or more of the filter capacitors Cab, Cbc and/or Cca according tothe calculated fundamental frequency filter capacitor impedance valuesZ_(ab.60Hz), Z_(bc.60Hz) and Z_(ca.60Hz). For example, certainimplementations of the detection system 70 individually compare thecapacitor impedance values Z_(ab.60Hz), Z_(bc.60Hz) and Z_(ca.60) Hz toone or more threshold values 76, such as a lower threshold value 76representing a nominal capacitance value minus a certain percentage aswell as an upper threshold value 76 representing the nominal capacitanceplus another percentage (e.g., 5-8% in one implementation) representingmanufacturing tolerances, temperature drift effects, component ageeffects, etc. If the calculated fundamental frequency impedance valueZ_(.60Hz) of any one of the capacitors Cab, Cbc and/or Cca goes belowthe lower threshold or above the upper threshold, the system 70 providesthe detection signal 78 to initiate a user alarm or alert and/or to shutdown the motor drive 10.

In certain implementations, the system 70 includes one or more hardwareand/or processor-executed software type filters 72 which filter theline-to-line voltages V_(c.ab), V_(c.bc) and V_(c.ca) and the filtercircuit branch currents I_(ca), I_(c.b) and I_(c.c) to obtain filteredline-to-line voltages V_(c.ab.60hz), V_(c.bc.60hz) and V_(c.c60hz) andfiltered circuit branch currents I_(c.a.60hz), I_(c.b.60hz) andI_(c.c.60hz) at a fundamental frequency of the multiphase AC inputpower. For example, the LPF/RMS component 72 may include a low passand/or bandpass filter or combinations thereof of any suitable order orfilter type to remove frequencies above the AC input power fundamentalfrequency (e.g., 60 Hz in one example). For example, certainimplementations employ a second order Butterworth low pass filter with acutoff frequency of about 80 Hz to obtain the filtered line-to-linevoltages V_(c.ab.60hz), V_(c.bc.60hz) and V_(c.ca60hz) and filteredcircuit branch currents I_(c.a.60hz), I_(c.b.60hz) and I_(c.c.60hz).

The component 72 also calculates RMS line-to-line voltagesV_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS) and V_(c.ca.60hz.RMS) according tothe filtered line-to-line voltages V_(c.ab.60hz), V_(c.bc.60hz) andI_(c.ca.60hz) and calculates RMS circuit branch currentsI_(c.a.60hz.RMS), I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS) according to thefiltered circuit branch currents I_(c.a.60hz), I_(c.b.60hz) andI_(c.c.60hz). The RMS computations can be according to any suitableroot-mean-square formulas as are known, such as calculating the squareroot of the mean of the squares of a series of sampled values of thefiltered voltage or current value (e.g., at the fundamental frequency).Moreover, the illustrated embodiment of the degradation detection system70 uses the impedance computation component 74 to calculate thefundamental frequency filter capacitor impedance values Z_(ab.60Hz),Z_(bc.60Hz) and Z_(ca.60Hz) according to the fundamental frequency RMSline-to-line voltages V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS) andV_(c.ca.60hz.RMS) and according to the fundamental frequency RMS circuitbranch currents I_(c.a.60hz.RMS), I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS)as described further below.

Referring also to FIG. 3, the exemplary system 70 advantageously employsa ratio type correction factor in the computation of the fundamentalfrequency filter capacitor impedance values, which is derived using anartificial resistive circuit shown connected to the capacitor circuitbranches 22. Although this resistive circuit is not in fact provided inthe motor drive 10 (illustrated instead in dashed-lines in FIG. 3), sucha delta-connected resistor network including 1 ohm resistor elementsRab1, Rbc1 and Rca1 provides a useful forum for developing a correctionfactor used with respect to the delta-connected filter capacitors Cab,Cbc and Cca of the filter circuit 20. As seen in FIGS. 1-3, while thebranch circuit currents I_(ca.), I_(c.b) and I_(c.c) can be directlymeasured by the feedback system of the motor drive 20 (along with thesensed line-to-line voltage values V_(c.ab), V_(c.bc) and V_(c.ca)), theleg circuit currents I_(c.ab), I_(c.bc) and I_(c.ca) actually flowingthrough the individual capacitors Cab, Cbc and Cca in the deltaconfiguration would require dedicated sensors, which would add cost tothe system 10 and/or which may not be feasible in view of packagingrequirements for the motor drive 10. Furthermore, the ability toaccurately compute the leg circuit currents I_(c.ab), I_(c.bc) andI_(c.ca) facilitates computation of the corresponding impedance valuesZ_(ab), Z_(bc) and Z_(ca), of the filter capacitors Cab, Cbc and Cca bydividing the line-to-line voltages by the calculated leg circuitcurrents I_(c.ab), I_(c.bc) and I_(c.ca).

In this regard, the inventors have appreciated that the best way topredict degradation of a capacitor is to monitor the capacitorimpedance, such as by comparison by the impedance computation component74 with one or more thresholds 76. Moreover, the impedance based on thefundamental frequency (e.g., 60 Hz) is preferred, since the presence ofthe filter circuit 20 within a switching power conversion system 10leads to higher frequency harmonic content. For example, in an activefront end motor drive, the fundamental frequency component willgenerally have the largest amplitude in a frequency spectrum, and theremainder of the significant harmonics (e.g., around 4 kHz and 8 kHz fora 4 kHz PWM switching frequency) will generally include a number ofdifferent harmonics close to one another, and are of generally loweramplitude, whereby it is more difficult to extract a signal forthreshold comparison with respect to the higher order harmonics.

Moreover, for metallized polypropylene capacitors such as are often usedin motor drive input filter circuits 20, the capacitance may vary acertain amount (e.g., +1.4% to −2.5%) over a relevant temperature range(e.g., −55° C. to +85° C.), in addition to an initial manufacturingtolerance of +/−3%, and a maximum tolerance over the operationallifetime of the capacitor component (aging tolerance), which factors canbe considered in setting the threshold or thresholds 76 used forcomparison with the computed filter capacitor impedance valuesZ_(ab.60Hz), Z_(bc.60Hz) and Z_(ca.60Hz). In one possibleimplementation, and initial impedance value is determined (e.g.,according to manufacturer's specifications, etc.), a lower threshold 76is set as a first constant multiplied by the initial impedance value(e.g., 0.9 in one case), and the initial value is multiplied by a secondconstant (e.g., 1.1) to obtain the upper threshold 76.

The inventors have further appreciated that the delta configuration ofthe filter capacitors as shown in FIGS. 1-3, and the inability orundesirability of adding dedicated current sensors to measure the legcircuit currents I_(c.ab), I_(c.bc) and I_(c.ca) actually flowingthrough the filter capacitors Cab, Cbc and Cca, can be mitigated orovercome by carefully adjusting or compensating calculations for thereal leg circuit currents I_(c.ab.), I_(c.bc) and I_(c.ca) according tofactors and/or parameters that can be directly measured and/or assumed.Specifically, as described below, the inventors have developedtechniques for computing the leg circuit currents I_(c.ab), I_(c.bc) andI_(c.ca) in terms of the sensed line-to-line voltages, the sensed branchcircuit currents I_(ca), I_(c.b) and I_(cc) as well as measured and/orassumed phase angles Φ_(bc) and Φ_(ca) between the line-to-line voltagesV_(c.ab) and V_(c.bc) across the filter capacitors Cab, Cbc. Thus, thetechniques and apparatus of the present disclosure overcome theinability or undesirability of additional dedicated filter capacitorcurrent sensing, while providing the ability to accurately monitor thecapacitance value of the filter capacitors Cab, Cbc and Cca fordetection or early warning of capacitor degradation.

As seen in FIG. 3, the artificial delta-connected resistance circuit iscoupled to the branch circuits 22 a, 22 b and 22 c (as is the actualdelta-connected filter capacitor circuitry). With respect to the RMScurrents flowing in the actual filter capacitor circuit, the followingequations (1) can be created according to Kirchhoffs current law at thethree circuit nodes a, b and c:

$\begin{matrix}\left. \begin{matrix}\begin{matrix}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} = {I_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}}}} \\{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} = {I_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}}}\end{matrix} \\{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} = {I_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}}}\end{matrix} \right\} & (1)\end{matrix}$

From equation (1), the following equations (2)-(4) can be derived forcalculated fundamental frequency RMS currents flowing in the capacitorsCab, Cbc and Cca:

$\begin{matrix}{I_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{{c.a.\; 60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b.\; 60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}{2}} & (2) \\{I_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{{c.b.\; 60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c.\; 60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}{2}} & (3) \\{I_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{{c.c.\; 60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a.\; 60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}{2}} & (4)\end{matrix}$

However, the inventors have appreciated that equations (1)-(4) do notexactly represent Kirchhoffs current law for the nodes of the filtercircuit because Kirchhoffs current law was not written for rms values,and thus the artificial resistive circuit shown in FIG. 3 is used toderive correction factors used by the impedance computation component 74in the motor drive 10. The artificial resistive circuit of FIG. 3demonstrates that the currents I_(ab1), I_(bc1), I_(ca1) in the legs ofthe resistive delta-connected circuit can be measured, assuming that theartificial circuit resistors R_(ab1), R_(bc1), R_(ca1) are known (e.g.,1 ohm to simplify the computations), and that the resistive circuitbranch currents I_(a1), I_(b1), I_(c1) can be measured. Using equations(2)-(4) above for calculating the artificial circuit currents I_(ab1),I_(bc1), I_(ca1), the following equations (5)-(7) can be derived:

$\begin{matrix}{I_{{ab}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{a\; 1.60\; {{hz}.{rms}}} + I_{b\; 1.60\mspace{11mu} {{hz}.{rms}}} - I_{c\; 1.60\; {{hz}.{rms}}}}{2}} & (5) \\{I_{{bc}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{b\; 1.60\; {{hz}.{rms}}} + I_{c\; 1.60\mspace{11mu} {{hz}.{rms}}} - I_{a\; 1.60\; {{hz}.{rms}}}}{2}} & (6) \\{I_{{ca}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}} = \frac{I_{c\; 1.60\mspace{11mu} {{hz}.{rms}}} + I_{a\; 1.60\mspace{11mu} {{hz}.{rms}}} - I_{b\; 1.60\; {{hz}.{rms}}}}{2}} & (7)\end{matrix}$

The real current in the delta-connected capacitor leg circuits can becomputed using the following ratios set forth in equations (8)-(10):

$\begin{matrix}{{Ratio}_{ab} = \frac{I_{{ab}\; 1.60\mspace{11mu} {{hz}.{rms}.{real}}}}{I_{{ab}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}}}} & (8) \\{{Ratio}_{bc} = \frac{I_{{bc}\; 1.60\mspace{11mu} {{hz}.{rms}.{real}}}}{I_{{bc}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}}}} & (9) \\{{Ratio}_{ca} = \frac{I_{{ca}\; 1.60\mspace{11mu} {{hz}.{rms}.{real}}}}{I_{{ca}\; 1.60\mspace{11mu} {{hz}.{rms}.{calc}}}}} & (10)\end{matrix}$

Using the ratios of equations (8)-(10), the real current in thedelta-connected filter capacitors can be computed according to thefollowing equations (11)-(13):

I _(c.ab.60hz.rms.real)=Ratio_(ab) ·I _(c.ab.60hz.rms.calc)  (11)

I _(c.bc.60hz.rms.real)=Ratio_(bc) ·I _(c.bc.60hz.rms.calc)  (12)

I _(c.ca.60hz.rms.real)=Ratio_(ca) ·I _(c.ca.60hz.rms.calc)  (13)

In addition, the fundamental frequency RMS filter capacitor impedancescan be computed according to the following equations (14)-(16) asfollows:

$\begin{matrix}{Z_{{ab}{.60}\mspace{11mu} {Hz}} = \frac{V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}}{I_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}.{real}}}}} & (14) \\{Z_{{bc}{.60}\mspace{11mu} {Hz}} = \frac{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}}{I_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}.{real}}}}} & (15) \\{Z_{{ca}{.60}\mspace{11mu} {Hz}} = \frac{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}}}{I_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}.{real}}}}} & (16)\end{matrix}$

As seen in FIG. 3, moreover, the leg currents in the artificialresistive network can be derived according to the following equations(17)-(19):

$\begin{matrix}\begin{matrix}{I_{{ab}\; 1.60\mspace{11mu} {{hz}.{real}}{.1}} = \frac{V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {\omega \; t} \right)}}{1}} \\{= {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {\omega \; t} \right)}}}\end{matrix} & (17) \\\begin{matrix}{I_{{bc}\; 1.60\mspace{11mu} {{hz}.{real}}{.1}} = \frac{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {{\omega \; t} - \phi_{bc}} \right)}}{1}} \\{= {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {{\omega \; t} - \phi_{bc}} \right)}}}\end{matrix} & (18) \\\begin{matrix}{I_{{ca}\; 1.60\mspace{11mu} {{hz}.{real}}{.1}} = \frac{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {{\omega \; t} - \phi_{ca}} \right)}}{1}} \\{= {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{peak}}} \cdot {{Sin}\left( {{\omega \; t} - \phi_{ca}} \right)}}}\end{matrix} & (19)\end{matrix}$

In addition, assuming the resistance value of 1 ohm, the followingequations (20)-(22) can be used to express the resistor currents as afunction of the measured voltages:

I _(ab1.60hz.real.1.rms) =V _(c.ab.60hz.rms)  (20)

I _(bc1.60hz.real.1.rms) =V _(c.bc.60hz.rms)  (21)

I _(ca1.60hz.real.1.rms) =V _(c.ca.60hz.rms)  (22)

where φ_(bc), φ_(ca) are the voltage phase angles in radians accordingto the graph 200 shown in FIG. 7. According to Kirchhoff's current lawfor the nodes of the artificial resistive circuit in FIG. 3, thefollowing equations (23)-(25) can be constructed:

I _(a1.60hz.calc.1) =I _(ab1.60hz.real.1) −I _(ca1.60hz.real.1)  (23)

where I_(a1-60hz.calc.1) is a calculated phase current withR_(ab1)=R_(bc1)=R_(ca1)=1

I _(b1.60hz.calc.1) =I _(bc1.60hz.real.1) −I _(ab1.60hz.real.1)  (24)

where I_(b1-60hz.calc.1) is a calculated phase current withR_(ab1)=R_(bc1)=R_(ca1)=1

I _(c1.60hz.calc.1) =I _(ca1.60hz.real.1) −I _(bc1.60hz.real.1)  (25)

where I_(c1-60hz.calc.1) is a calculated phase current withR_(ab1)=R_(bc1)=R_(ca1)=1

Substituting equations (17)-(19) into equations (23)-(25) yields thefollowing equations (26)-(28):

$\begin{matrix}{\mspace{79mu} {I_{a\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = \sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}}}} & (26) \\{\mspace{79mu} {I_{b\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = \sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}}}} & (27) \\{I_{c\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = \sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}}} & (28)\end{matrix}$

Equations (26)-(28) represent the RMS current values in thedelta-connected resistors of the artificial network in FIG. 3. Fromthese, the calculated currents in the legs of the delta-connectedartificial resistor network can be determined according to the followingequations (29)-(31):

$\begin{matrix}{I_{{ab}\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = {\frac{1}{2} \cdot \begin{bmatrix}{\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}} +} \\\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}} -} \\\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}}\end{matrix}\end{bmatrix}}} & (29) \\{I_{{bc}\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = {\frac{1}{2} \cdot \begin{bmatrix}\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -}\end{matrix} \\\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}}\end{bmatrix}}} & (30) \\{I_{{ca}\; 1.60\mspace{11mu} {{hz}.{calc}}{{.1}.{rms}}} = {\frac{1}{2} \cdot \begin{bmatrix}\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} +} \\{\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\; {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}} -}\end{matrix} \\\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}}\end{bmatrix}}} & (31)\end{matrix}$

Correction factors (ratios) can then be calculated based on the aboveequations, to derive the following equations (32)-(34) as follows:

$\begin{matrix}{{Ratio}_{{{ab}.{calc}}{.1}} = \frac{2 \cdot V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}}{\left\lbrack \begin{matrix}\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}} -}\end{matrix} \\\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}}\end{matrix} \right\rbrack}} & (32) \\{{Ratio}_{{{bc}.{calc}}{.1}} = \frac{2 \cdot V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}}{\left\lbrack \begin{matrix}\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -}\end{matrix} \\\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}}\end{matrix} \right\rbrack}} & (33) \\{{Ratio}_{{{ca}.{calc}}{.1}} = \frac{2 \cdot V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}}}{\left\lbrack \begin{matrix}\begin{matrix}{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} +} \\{\sqrt{\begin{matrix}{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}} -}\end{matrix} \\\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}}\end{matrix} \right\rbrack}} & (34)\end{matrix}$

c

Applying these ratios with respect to the leg currents flowing in thedelta-connected filter capacitors Cab, Cbc, and Cca, the followingequations (35)-(37) can be derived:

$\begin{matrix}{Z_{{ab}{.60}\mspace{14mu} {Hz}} = \frac{\begin{bmatrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{14mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} -} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}\end{bmatrix}}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}} & (35) \\{Z_{{bc}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}\;} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -} \\\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}} & (36) \\{Z_{{ca}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}++} \\\begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}--} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}} & (37)\end{matrix}$

As seen in FIG. 6, In certain embodiments, the impedance computationcomponent 74 employs the above equations 74ab, 74 bc and 74 ca((35)-(37)) to compute the fundamental frequency filter capacitorimpedance values Z_(ab.60Hz), Z_(bc.60Hz) and Z_(ca.60Hz) according tothe RMS line-to-line voltages V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS) andV_(c.ca.60hz.RMS) and according to the RMS circuit branch currentsI_(c.a.60hz.RMS), I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS). Moreover, thedegradation detection system 70 in certain embodiments may include azero-crossing detection circuit operative to measure the phase anglesΦ_(bc), Φ_(ca) between the line-to-line voltages V_(c.ab) and V_(c.bc)across the filter capacitors Cab and Cbc for use in computing thefundamental frequency filter capacitor impedance values Z_(ab.60Hz),Z_(bc.60Hz) and Z_(ca.60Hz). In other possible implementations, thesystem 70 may employ assumed values of the phase angles Φ_(bc) andΦ_(ca), for example, 120° and 240°, to calculate the fundamentalfrequency filter capacitor impedance values Z_(ab.60Hz), Z_(bc.60Hz),Z_(ca.60Hz) using the above equations (35)-(37). In this case, it isnoted that the cosine and sine values of these angles can be precomputedas follows:

Cos(φ_(bc))=Cos(φ_(ca))=Cos(120°)=Cos(240°)=−0.5;

Sin(φ_(bc))=Sin(120°)=0.866;

Sin(φ_(ca))=Sin(240°)=−0.866.

The inventors have appreciated that the described techniques areindependent of voltage unbalance conditions, and are furtheradvantageous in that individually calculated capacitor impedance valuescan be separately compared with one or more thresholds 76. Accordingly,a separate assessment of the relative health and/or degradation of theindividual filter capacitors can be performed, allowing selectiveidentification of which filter capacitor (if any) is degrading.

Referring also to FIGS. 4 and 5, an exemplary process 100 is illustratedfor detecting filter capacitor degradation in accordance with furtheraspects of the present disclosure. The process 100 begins at 102 in FIG.4, where line-to-line voltages V_(c.ab), V_(c.bc) and V_(c.ca) acrossfilter capacitors Cab, Cbc and Cca are measured. At 104, these measuredvoltages are filtered to obtain filtered line-to-line voltagesV_(c.ab.60hz), V_(c.bc.60hz) and V_(c.ca.60hz) at the fundamentalfrequency of the multiphase AC input power (e.g., 60 Hz). At 106, RMSline-to-line voltages V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS) andV_(c.ca.60hz.RMS) are calculated according to the filtered line-to-linevoltages V_(c.ab.60hz), V_(c.bc.60hz) and V_(c.ca.60hz). At 108, thefilter circuit branch currents I_(c.a), I_(c.b) and I_(c.c) are measuredin the capacitor circuit branches 22 a, 22 b, 22 c, and these values arefiltered at 110 and RMS values are computed at 112. At 114 in FIG. 4,the phase angles Φ_(bc), Φ_(ca) between the line-to-line voltagesV_(c.ab) and V_(c.bc) across the filter capacitors Cab and Cbc can bemeasured or assumed as discussed above, and the ratios characterizingthe real versus calculated RMS delta circuit leg current values can becomputed according to the RMS line-to-line voltages at the fundamentalfrequency and the measured or assumed phase angles (e.g., ratios andequations (32)-(34) above).

As seen in FIG. 5, the process 100 further includes calculating the realdelta circuit RMS filter leg currents at the fundamental frequencyaccording to the calculated fundamental frequency currents and accordingto the ratios determined at 116. At 120, the fundamental frequencyfilter capacitor impedance values Z_(ab.60Hz), Z_(bc.60Hz) andZ_(ca.60Hz) are calculated based at least in part on the line-to-linevoltages V_(c.ab), V_(c.bc) and V_(c.ca) and according to the filtercircuit branch currents I_(c.a), I_(c.b) and I_(c.c), and these arecompared at 122 with at least one threshold 76. At 124, an alert isissued or the power converter is shut down if one or more of thecapacitor impedance values exceeds the threshold(s), and the process 100returns again to 102 in FIG. 4 as described above.

Referring also to FIGS. 8-10, another motor drive power conversionsystem embodiment 10 is shown in FIG. 8, with an LCL filter 20, arectifier 30, intermediate DC link circuit 40 and inverter 50 operatedby a motor drive controller 60 generally as described above to power amotor or other AC load 6 using power from an AC input source 2. In thiscase, however, the LCL filter 20 includes series circuits individuallyincluding two series-connected inductors (La and Lu, etc.) withcorresponding capacitor circuit branches 22 connecting the seriescircuits with three filter capacitors Ca, Cb and Cc connected in a Yconfiguration with each filter capacitor C connected between acorresponding one of the capacitor circuit branches 22 and a commonconnection node 24. Other embodiments are possible in which only asingle inductor is provided in each of the series circuits, such aswhere the motor drive 10 is used in combination with an inputtransformer (e.g., as shown in FIG. 2 above). The feedback circuit inFIGS. 8 and 9, moreover, is operative to sense capacitor voltagesV_(c.a), V_(c.b) and V_(c.c) across the filter capacitors Ca, Cb and Cc(e.g., between the corresponding node a, b or c and the commonconnection node 24). Also, the feedback senses the filter circuit branchcurrents I_(c.a), I_(c.b) and I_(c.c) flowing in the capacitor circuitbranches 22 a, 22 b and 22 c. The filter capacitor degradation detectionsystem 70 in this case calculates fundamental frequency filter capacitorimpedance values Z_(a.60Hz), Z_(b.60Hz) and Z_(c.60Hz) based at leastpartially on the capacitor voltages V_(c.a), V_(c.b) and V_(c.c) as wellas the filter circuit branch currents I_(c.a), I_(c.b) and I_(c.c), andselectively detects degradation of one or more of the filter capacitorsCa, Cb and Cc according to the calculated fundamental frequency filtercapacitor impedance values Z_(a.60Hz), Z_(b.60Hz) and/or Z_(c.60Hz). forinstance, the system 70 may individually compare the computed impedancevalues Z_(a.60Hz), Z_(b.60Hz) and Z_(c.60Hz) with one or more thresholds76 as described above in connection with FIGS. 1-5.

FIG. 10 illustrates a process 300 for filter capacitor degradationdetection, which may be implemented in the system 70 of FIG. 8: At 302,the capacitor voltages V_(c.a), V_(c.b) and V_(c.c) are measured, andthese are filtered at 304, for example, using any suitable bandpassand/or low pass filtering (e.g., second order Butterworth low passfilter with a cutoff frequency of 80 Hz in one example), in order toobtain fundamental frequency capacitor voltage values V_(c.a.60hz),V_(c.b.60hz) and V_(c.c.60hz). At 306 in FIG. 10, RMS valuesV_(c.a.60hz.RMS), V_(c.b.60hz.RMS) and V_(c.c60hz.RMS) of thefundamental frequency voltages are calculated, for example, using theabove described or any other suitable RMS computation techniques. At308, the phase currents I_(c.a), I_(c.b) and I_(c.c) are measured, andthese are filtered at 310 to obtain filtered circuit branch currentsI_(c.a.60hz), I_(c.b.60hz) and I_(c.c.60hz) at the input powerfundamental frequency (e.g., 60 Hz). At 312, RMS circuit branch currentsI_(c.a.60hz.RMS), I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS) are calculatedaccording to the filtered circuit branch currents I_(c.a.60hz),I_(c.b.60hz) and I_(c.c.60hz). The fundamental frequency filtercapacitor impedance values Z_(a.60Hz), Z_(b.60Hz) and Z_(c.60Hz) arecalculated at 314 as ratios of the RMS voltages V_(c.a.60hz.RMS),V_(c.b.60hz.RMS) and V_(c.c60hz.RMS) to the corresponding RMS currentsI_(c.a.60hz.RMS), I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS) according to thefollowing formula (38):

$\begin{matrix}{Z_{c{.60}\mspace{11mu} {{Hz}.{RMS}}} = {\frac{V_{c{.60}\mspace{14mu} {{HZ}.{RMS}}}}{I_{c{.60}\mspace{14mu} {{Hz}.{RMS}}}}.}} & (38)\end{matrix}$

The inventors have appreciated that the RMS computations at 306 and 312advantageously avoid situations where the sampled and filtered currentfundamental frequency sinusoidal currents I_(c.60hz) or the voltagesV_(c.a.60hz) pass through zero, causing the non-RMS ratio equation tobecome unreliable for determining the actual capacitor values. At 316 inFIG. 10, the capacitor impedance values Z_(a.60Hz), Z_(b.60Hz) andZ_(c.60Hz) are individually compared with one or more thresholds 76, andthe system 70 can issue an alert is a signal or message 78 and/or shutdown the drive 10 at 318 based on the threshold comparisons.

The above embodiments and variants thereof facilitate determination of apoint where one or more filter capacitors of the input filter 20 maybegin to degrade, and the threshold value or values 76 can be stored inthe detection system 70 in the above embodiments. In certainimplementations, the threshold values 76 can be determined by the systembased on an initial capacitance value measurement, and/or may be setaccording to manufacturer's specifications including manufacturingtolerances, temperature effects, aging effects, etc. In the illustratedembodiments, the calculated capacitor impedance values Z_(a.60Hz),Z_(b.60Hz) and Z_(c.60Hz) are effectively compared with initialcapacitance values (measured or specified) Z_(c.a.initial),Z_(c.b.initial), Z_(c.c.initial) and the thresholds 76 can be determinedrelative to the initial values. For instance, the threshold values maybe computed in terms of multipliers are constants multiplied by theinitial impedance values. In one possible embodiment, a lower thresholdis set according to a first constant (e.g., 0.9) multiplied by theinitial capacitance value, and an upper threshold 76 could be 1.1 timesthe initial value, with the system 70 selectively issuing a detectionsignal 78 if the measured impedance value falls below the lowerthreshold or rises above the upper threshold.

The above examples are merely illustrative of several possibleembodiments of various aspects of the present disclosure, whereinequivalent alterations and/or modifications will occur to others skilledin the art upon reading and understanding this specification and theannexed drawings. In particular regard to the various functionsperformed by the above described components (assemblies, devices,systems, circuits, and the like), the terms (including a reference to a“means”) used to describe such components are intended to correspond,unless otherwise indicated, to any component, such as hardware,processor-executed software, or combinations thereof, which performs thespecified function of the described component (i.e., that isfunctionally equivalent), even though not structurally equivalent to thedisclosed structure which performs the function in the illustratedimplementations of the disclosure. In addition, although a particularfeature of the disclosure may have been disclosed with respect to onlyone of several implementations, such feature may be combined with one ormore other features of the other implementations as may be desired andadvantageous for any given or particular application. Also, to theextent that the terms “including”, “includes”, “having”, “has”, “with”,or variants thereof are used in the detailed description and/or in theclaims, such terms are intended to be inclusive in a manner similar tothe term “comprising”.

1. A power conversion system, comprising: a power converter inputoperative to receive multiphase AC input power; an active front end(AFE) rectifier, comprising a three phase AC input, and a plurality ofswitching devices operative according to a plurality of rectifierswitching control signals to convert power received at the three phaseAC input to provide DC output power; an input filter circuit coupledbetween the power converter input and the AFE rectifier, the inputfilter circuit comprising first, second, and third series circuitsindividually including at least one filter inductor coupled between acorresponding phase of the power converter input and a correspondingphase of the three phase AC input of the AFE rectifier, first, second,and third capacitor circuit branches respectively connected to thefirst, second and third series circuits, and three filter capacitorsconnected in a delta configuration with each filter capacitor connectedto two of the capacitor circuit branches; a feedback circuit operativelycoupled with the input filter circuit to sense line-to-line voltagesacross the filter capacitors and filter circuit branch currents flowingin the capacitor circuit branches; and a degradation detection systemoperatively coupled with the input filter circuit to calculatefundamental frequency filter capacitor impedance values at leastpartially according to the line-to-line voltages and according to thefilter circuit branch currents, and to selectively detect degradation ofone or more of the filter capacitors according to the calculatedfundamental frequency filter capacitor impedance values.
 2. The powerconversion system of claim 1: wherein the individual series circuits ofthe input filter circuit include a first filter inductor connected tothe corresponding phase of the power converter input and a second filterinductor connected between the first filter inductor and thecorresponding phase of the three phase AC input of the AFE rectifier;and wherein the individual capacitor circuit branches of the inputfilter circuit are connected to a node joining the first and secondfilter inductors of the corresponding series circuit.
 3. The powerconversion system of claim 2, wherein the degradation detection systemis operative to: filter the line-to-line voltages and the filter circuitbranch currents to obtain filtered line-to-line voltages and filteredcircuit branch currents at a fundamental frequency of the multiphase ACinput power; calculate RMS line-to-line voltages according to thefiltered line-to-line voltages; calculate RMS circuit branch currentsaccording to the filtered circuit branch currents; and calculate thefundamental frequency filter capacitor impedance values according to theRMS line-to-line voltages and according to the RMS circuit branchcurrents.
 4. The power conversion system of claim 3, wherein thedegradation detection system is operative to: calculate the fundamentalfrequency filter capacitor impedance value Z_(ab.60Hz) of a first filtercapacitor according to the following equation:${Z_{{ab}{.60}\mspace{14mu} {Hz}} = \frac{\begin{bmatrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{14mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} -} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}\end{bmatrix}}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}};$calculate the fundamental frequency filter capacitor impedance valueZ_(bc.60Hz) of a second filter capacitor according to the followingequation:${Z_{{bc}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}\;} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -} \\\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}};$and calculate the fundamental frequency filter capacitor impedance valueZ_(ca.60Hz) of a third filter capacitor according to the followingequation:${Z_{{ca}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}++} \\\begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}--} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}};$wherein V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS), and V_(c.ca.60hz.RMS), arethe RMS line-to-line voltages across the first, second, and third filtercapacitors, respectively; I_(c.a.60hz.RMS)) I_(c.b.60hz.RMS), andI_(c.c.60hz.RMS) are the RMS circuit branch currents flowing through thefirst, second, and third circuit branches, respectively; Φ_(bc) is aphase angle between the line-to-line voltages across the first andsecond filter capacitors; and Φ_(ca) is a phase angle between theline-to-line voltages across the first and third filter capacitors. 5.The power conversion system of claim 4, wherein the degradationdetection system comprises a zero-crossing detection circuit to measurethe phase angles between the line-to-line voltages across the filtercapacitors.
 6. The power conversion system of claim 4, wherein thedegradation detection system uses assumed values of the phase anglesbetween the line-to-line voltages across the filter capacitors tocalculate the fundamental frequency filter capacitor impedance values.7. The power conversion system of claim 1, wherein the degradationdetection system is operative to: filter the line-to-line voltages andthe filter circuit branch currents to obtain filtered line-to-linevoltages and filtered circuit branch currents at a fundamental frequencyof the multiphase AC input power; calculate RMS line-to-line voltagesaccording to the filtered line-to-line voltages; calculate RMS circuitbranch currents according to the filtered circuit branch currents; andcalculate the fundamental frequency filter capacitor impedance valuesaccording to the RMS line-to-line voltages and according to the RMScircuit branch currents.
 8. The power conversion system of claim 7,wherein the degradation detection system is operative to: calculate thefundamental frequency filter capacitor impedance value Z_(ab.60Hz) of afirst filter capacitor according to the following equation:${Z_{{ab}{.60}\mspace{14mu} {Hz}} = \frac{\begin{bmatrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{14mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} -} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}\end{bmatrix}}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}};$calculate the fundamental frequency filter capacitor impedance valueZ_(bc.60Hz) of a second filter capacitor according to the followingequation:${Z_{{bc}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}\;} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -} \\\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}};$and calculate the fundamental frequency filter capacitor impedance valueZ_(ca.60Hz) of a third filter capacitor according to the followingequation:${Z_{{ca}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}++} \\\begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}--} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}};$wherein V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS), and V_(c.ca.60hz.RMS), arethe RMS line-to-line voltages across the first, second, and third filtercapacitors, respectively; I_(c.a.60hz.RMS), I_(c.b.60hz.RMS), andI_(c.c.60hz.RMS) are the RMS circuit branch currents flowing through thefirst, second, and third circuit branches, respectively; Φ_(bc) is aphase angle between the line-to-line voltages across the first andsecond filter capacitors; and Φ_(ca) is a phase angle between theline-to-line voltages across the first and third filter capacitors. 9.The power conversion system of claim 8, wherein the degradationdetection system comprises a zero-crossing detection circuit to measurethe phase angles between the line-to-line voltages across the filtercapacitors.
 10. The power conversion system of claim 8, wherein thedegradation detection system uses assumed values of the phase anglesbetween the line-to-line voltages across the filter capacitors tocalculate the fundamental frequency filter capacitor impedance values.11. A method for detecting filter capacitor degradation in an activefront end (AFE) motor drive, the method comprising: measuringline-to-line voltages across filter capacitors connected in a deltaconfiguration with each filter capacitor connected to two of threecapacitor circuit branches in a filter circuit of the motor drive;measuring filter circuit branch currents flowing in the capacitorcircuit branches; calculating fundamental frequency filter capacitorimpedance values at least partially according to the line-to-linevoltages and according to the filter circuit branch currents; comparingthe calculated fundamental frequency filter capacitor impedance valueswith at least one threshold; and selectively detecting degradation ofone or more of the filter capacitors at least partially according to thecomparison of the calculated fundamental frequency filter capacitorimpedance values with the at least one threshold.
 12. The method ofclaim 11, further comprising issuing an alert or shutting down the motordrive at least partially according to the comparison of the calculatedfundamental frequency filter capacitor impedance values with the atleast one threshold.
 13. The method of claim 12, comprising: filteringthe measured line-to-line voltages to obtain filtered line-to-linevoltages at a fundamental frequency of the multiphase AC input power;calculating RMS line-to-line voltages according to the filteredline-to-line voltages; filtering the measured filter circuit branchcurrents to obtain filtered circuit branch currents at the fundamentalfrequency of the multiphase AC input power; calculating RMS circuitbranch currents according to the filtered circuit branch currents; andcalculating the fundamental frequency filter capacitor impedance valuesat least partially according to the RMS line-to-line voltages and theRMS circuit branch currents.
 14. The method of claim 13, comprising:calculating the fundamental frequency filter capacitor impedance valueZ_(ab.60Hz) of a first filter capacitor according to the followingequation: ${Z_{{ab}{.60}\mspace{14mu} {Hz}} = \frac{\begin{bmatrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{14mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} -} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}\end{bmatrix}}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}};$calculating the fundamental frequency filter capacitor impedance valueZ_(bc.60Hz) of a second filter capacitor according to the followingequation:${Z_{{bc}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}\;} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -} \\\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}};$and calculating the fundamental frequency filter capacitor impedancevalue Z_(ca.60Hz) of a third filter capacitor according to the followingequation:${Z_{{ca}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}++} \\\begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}--} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}};$wherein V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS), and V_(c.ca60hz.RMS), arethe RMS line-to-line voltages across the first, second, and third filtercapacitors, respectively; I_(c.a.60hz.RMS), I_(c.b.60hz.RMS), andI_(c.c.60hz.RMS) are the RMS circuit branch currents flowing through thefirst, second, and third circuit branches, respectively; Φ_(bc) is aphase angle between the line-to-line voltages across the first andsecond filter capacitors; and Φ_(ca) is a phase angle between theline-to-line voltages across the first and third filter capacitors. 15.The method of claim 11, comprising: filtering the measured line-to-linevoltages to obtain filtered line-to-line voltages at a fundamentalfrequency of the multiphase AC input power; calculating RMS line-to-linevoltages according to the filtered line-to-line voltages; filtering themeasured filter circuit branch currents to obtain filtered circuitbranch currents at the fundamental frequency of the multiphase AC inputpower; calculating RMS circuit branch currents according to the filteredcircuit branch currents; and calculating the fundamental frequencyfilter capacitor impedance values at least partially according to theRMS line-to-line voltages and the RMS circuit branch currents.
 16. Themethod of claim 15, comprising: calculating the fundamental frequencyfilter capacitor impedance value Z_(ab.60Hz) of a first filter capacitoraccording to the following equation:${Z_{{ab}{.60}\mspace{14mu} {Hz}} = \frac{\begin{bmatrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{14mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} -} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}\end{bmatrix}}{I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}}}};$calculating the fundamental frequency filter capacitor impedance valueZ_(bc.60Hz) of a second filter capacitor according to the followingequation:${Z_{{bc}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}}\;} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix} +} \\{\sqrt{\begin{matrix}{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{14mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}} -} \\\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}}}};$and calculating the fundamental frequency filter capacitor impedancevalue Z_(ca.60Hz) of a third filter capacitor according to the followingequation:${Z_{{ca}{.60}\mspace{14mu} {Hz}} = \frac{\left\lbrack \begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}} - {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}}} \right\rbrack^{2}\end{matrix}++} \\\begin{matrix}{\begin{matrix}\sqrt{\left\lbrack {V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}} - {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{ca} \right)}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{ca}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{ca} \right)}} \right\rbrack^{2}\end{matrix}--} \\\begin{matrix}\sqrt{\left\lbrack {{V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Cos}\left( \phi_{bc} \right)}} - V_{{c.{ab}}{.60}\mspace{11mu} {{hz}.{rms}}}} \right\rbrack^{2} +} \\\left\lbrack {V_{{c.{bc}}{.60}\mspace{11mu} {{hz}.{rms}}} \cdot {{Sin}\left( \phi_{bc} \right)}} \right\rbrack^{2}\end{matrix}\end{matrix}\end{matrix} \right\rbrack}{I_{{c.c}{.60}\mspace{11mu} {{hz}.{rms}}} + I_{{c.a}{.60}\mspace{11mu} {{hz}.{rms}}} - I_{{c.b}{.60}\mspace{11mu} {{hz}.{rms}}}}};$wherein V_(c.ab.60hz.RMS), V_(c.bc.60hz.RMS), and V_(c.ca.60hz.RMS), arethe RMS line-to-line voltages across the first, second, and third filtercapacitors, respectively; I_(c.a.60hz.RMS), I_(c.b.60hz,RMS), andI_(c.c.60hz.RMS) are the RMS circuit branch currents flowing through thefirst, second, and third circuit branches, respectively; Φ_(bc) is aphase angle between the line-to-line voltages across the first andsecond filter capacitors; and Φ_(ca) is a phase angle between theline-to-line voltages across the first and third filter capacitors. 17.A power conversion system, comprising: a power converter input operativeto receive multiphase AC input power; an active front end (AFE)rectifier, comprising a three phase AC input, and a plurality ofswitching devices operative according to a plurality of rectifierswitching control signals to convert power received at the three phaseAC input to provide DC output power; an input filter circuit coupledbetween the power converter input and the AFE rectifier, the inputfilter circuit comprising first, second, and third series circuitsindividually including at least one filter inductor coupled between acorresponding phase of the power converter input and a correspondingphase of the three phase AC input of the AFE rectifier, first, second,and third capacitor circuit branches respectively connected to thefirst, second and third series circuits, and three filter capacitorsconnected in a Y configuration with each filter capacitor connectedbetween a corresponding one of the capacitor circuit branches and acommon connection node; a feedback circuit operatively coupled with theinput filter circuit to sense capacitor voltages across the filtercapacitors and filter circuit branch currents flowing in the capacitorcircuit branches; and a degradation detection system operatively coupledwith the input filter circuit to calculate fundamental frequency filtercapacitor impedance values at least partially according to the capacitorvoltages and according to the filter circuit branch currents, and toselectively detect degradation of one or more of the filter capacitorsaccording to the calculated fundamental frequency filter capacitorimpedance values.
 18. The power conversion system of claim 17: whereinthe individual series circuits of the input filter circuit include afirst filter inductor connected to the corresponding phase of the powerconverter input and a second filter inductor connected between the firstfilter inductor and the corresponding phase of the three phase AC inputof the AFE rectifier; and wherein the individual capacitor circuitbranches of the input filter circuit are connected to a node joining thefirst and second filter inductors of the corresponding series circuit.19. The power conversion system of claim 17, wherein the degradationdetection system is operative to: filter the measured capacitor voltagesand the filter circuit branch currents to obtain filtered capacitorvoltages and filtered circuit branch currents at a fundamental frequencyof the multiphase AC input power; calculate RMS capacitor voltagesaccording to the filtered line-to-line voltages; calculate RMS circuitbranch currents according to the filtered circuit branch currents; andcalculate the fundamental frequency filter capacitor impedance valuesaccording to the RMS capacitor voltages and according to the RMS circuitbranch currents.
 20. The power conversion system of claim 19, whereinthe degradation detection system is operative to calculate theindividual fundamental frequency filter capacitor impedance valuesZ_(a.60Hz), Z_(b.60Hz) and Z_(c.60Hz) as ratios of the RMS capacitorvoltages V_(c.a.60hz.RMS), V_(c.b.60hz.RMS) and V_(c.c.60hz.RMS) to thecorresponding RMS circuit branch currents I_(c.a.60hz.RMS),I_(c.b.60hz.RMS) and I_(c.c.60hz.RMS) according to the followingformula:$Z_{c{.60}\mspace{11mu} {{Hz}.{RMS}}} = {\frac{V_{c{.60}\mspace{14mu} {{HZ}.{RMS}}}}{I_{c{.60}\mspace{14mu} {{Hz}.{RMS}}}}.}$